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Delocalized Chern character for stringy orbifold K-theory


Authors: Jianxun Hu and Bai-Ling Wang
Journal: Trans. Amer. Math. Soc. 365 (2013), 6309-6341
MSC (2010): Primary 57R19, 19L10, 22A22; Secondary 55N15, 53D45
DOI: https://doi.org/10.1090/S0002-9947-2013-05834-5
Published electronically: June 4, 2013
MathSciNet review: 3105753
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Abstract: In this paper, we define a stringy product on $ K^*_{orb}(\mathfrak{X}) \otimes \mathbb{C}$, the orbifold K-theory of any almost complex presentable orbifold $ \mathfrak{X}$. We establish that under this stringy product, the delocalized Chern character

$\displaystyle ch_{deloc} : K^*_{orb}(\mathfrak{X}) \otimes \mathbb{C} \longrightarrow H^*_{CR}(\mathfrak{X}), $

after a canonical modification, is a ring isomorphism. Here $ H^*_{CR}(\mathfrak{X})$ is the Chen-Ruan cohomology of $ \mathfrak{X}$. The proof relies on an intrinsic description of the obstruction bundles in the construction of the Chen-Ruan product. As an application, we investigate this stringy product on the equivariant K-theory $ K^*_G(G)$ of a finite group $ G$ with the conjugation action. It turns out that the stringy product is different from the Pontryagin product (the latter is also called the fusion product in string theory).

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Additional Information

Jianxun Hu
Affiliation: Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, People’s Republic of China
Email: stsjxhu@mail.sysu.edu.cn

Bai-Ling Wang
Affiliation: Department of Mathematics, Australian National University, Canberra ACT 0200, Australia
Email: bai-ling.wang@anu.edu.au

DOI: https://doi.org/10.1090/S0002-9947-2013-05834-5
Keywords: Orbifold K-theory, delocalized Chern character, Chen-Ruan cohomology
Received by editor(s): October 5, 2011
Received by editor(s) in revised form: March 19, 2012
Published electronically: June 4, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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